# What each decision buys

> The five comparisons at the heart of the repair study, worked through: blind random destroy wins while every conflict-targeting operator loses; construction sets the floor; simulated annealing is the strongest acceptance rule; and the clever refinements (exact refill, restarts) buy nothing at this budget.

- Canonical page (with interactive figures/demos): https://eternity2.dev/research/lab/experiments/raphael-anjou/repair-study/findings/
- Updated: 2026-07-16
- Topics: local-search, search-space, speed
- Source: Committed per-run results (results.jsonl) and per-family report (report.md) — https://github.com/raphael-anjou/eternity2/tree/main/research/experiments/repair-study/results

---
Five comparisons carry the [repair study](/research/lab/experiments/raphael-anjou/repair-study).
Each isolates one decision by holding the other four fixed at a plain anchor loop:
greedy start, destroy the mismatched cells, greedy refill, keep the result unless
it loses score, never restart. All scores are the mean matched-edge count over the
ten corner-pinned variants, single core, sixty seconds. Iteration rate is never
compared across families.

## The starting board: the lever the loop cannot replace

Change only the board the loop begins from, and everything else about the run is
downstream of it. A greedy construction begins around 348 and the loop lifts it
to a mean of 366. A random board begins near 18 and the loop lifts it an enormous
308 points, to a mean of 326. That larger lift is not the loop doing better; it is
the loop doing the construction's job badly. The random start, after millions of
iterations, still finishes below where the greedy start *began*.

This is the study's first and firmest result: **construction is the lever, repair
is the polish.** A rarest-colour-first greedy construction (the Selby and Riordan
heuristic that a scarce colour should be spent where it is forced) starts a little
higher still and finishes at a mean of 373, the best of the *greedy* starts.

The clearest proof of the point is to start from a genuinely strong board rather
than a greedy one. The final starting-board variant hands the loop a board built
by the [DFS study's](/research/lab/experiments/raphael-anjou/dfs-study) break-DFS:
the run spends its first twenty seconds backtracking to a board in the low 440s,
then repairs it for the remaining forty. That start is a hundred points above a
greedy construction, and it carries straight through to the finish. It is the
highest-scoring variant in the whole study, at a mean of 446 (best 449), far above
the random-destroy loop's 402, and it settles the construct-then-refine question the
rest of the study circles: repair *does* add a few edges on top of a strong
backtracked board, but only a few, and the board it starts from decides almost
everything. This is exactly the division of labour the records use, and this study
reproduces it end to end on one core in one minute: a backtracker to build a good
board, then a repair loop to squeeze the last edges out of it.

## The destroy operator: attacking the breaks can backfire

Now fix the greedy start and change only which cells each iteration lifts. This is
the axis with the study's most surprising result.

> **[Figure]** The four destroy operators, on one board of broken seams — interactive: DestroyOperatorDiagram. Rendered on the canonical page (link above); not shown in this markdown export.

- **A geometry-blind random destroy wins the destroy comparison, at a mean of 402
  (best 409).** Lifting twelve *random* cells instead of the broken ones, it keeps
  sampling fresh regions of the board, accepts nearly three quarters of its moves,
  and its best score keeps improving deep into the run: its last improvement lands
  past three million iterations, where every conflict-driven variant has long since
  frozen. It is the best of every variant that starts from a greedy board (only the
  DFS-seeded start, a different lever entirely, finishes higher).
- **Every conflict-driven operator finishes below it, and the more it fixates on
  the breaks, the worse it does.** The mismatched-cells anchor, which lifts up to
  a dozen of the broken cells, averages 366 and stalls early: it rips out the same
  clustered tangle, greedily rebuilds it to almost the same placement, and its best
  score stops moving within a few thousand iterations. The component-plus-halo
  operator, which lifts one whole connected tangle (a much larger hole), does worse
  still, at 350, and its best last improves at iteration 211: a hole that size hands
  the greedy refill a subproblem it cannot improve, so almost nothing is ever kept.
- **A whole-band destroy is inert.** Lifting the two rows with the most breaks
  leaves the greedy refill a subproblem nearly as hard as the puzzle itself; on
  nine of the ten instances it makes *zero* improvements over the whole minute, so
  its reported score is simply its starting board.

The pattern is clean and worth stating plainly: on this mediocre greedy start,
the more precisely an operator targets the existing breaks, the worse it does, and
blind random destroy wins. This is the opposite of the natural intuition, and of
what works on a *near-record* board, where the whole board is close to optimal and
the community's tuning found conflict-driven and component operators most valuable
precisely because the few remaining mismatches are the only thing left to fix. This
study never reaches that regime. Sixty seconds on a mediocre board leaves broad
improvement available everywhere, and there an operator that keeps re-attacking the
same broken cluster, or that tears out a hole too large to rebuild well, both lose
to one that simply keeps trying fresh small regions. The finding is not
"conflict-driven destroy is bad" but "which operator wins depends on how good the
board already is, and on a mediocre board, exploring beats both fixating and
over-destroying."

## Repair: how the hole is rebuilt

Fix the destroy and change only the refill. Breaking the greedy refill's exact
score ties with a seeded coin, rather than deterministically, adds a little
exploration and helps slightly, to a mean of 365. The sharper comparison is greedy
against *exact* refill, and it has to be set up carefully to be a clean one-axis
test: the exact refill only pays off when the hole is small enough to search, so
the study pairs it with a small destroy (at most six mismatched cells) and compares
it against the *same* small destroy refilled greedily, so the only thing that
changes between the two is the refill. Set up this way, the exact refill runs on
every iteration rather than falling back to greedy, rebuilding each small hole to
its true optimum.

The result is a clean negative one. The exact refill (mean 360) does **not** beat
the greedy refill of the same small hole (mean 363); if anything it is a shade
behind. Two things explain it. The exact refill accepts nearly every iteration,
because a locally-optimal rebuild of a six-cell hole almost never lowers the score,
so the loop drifts sideways rather than climbing. And it buys that local optimality
at roughly a third of the iteration count, so over a fixed minute it explores less
of the board. On this puzzle, at this budget, a locally-perfect rebuild of a tiny
region is not worth what it costs: the greedy refill's cheaper, slightly worse
rebuilds, run more often, reach just as far. This is the same node-rate-is-not-score
question the DFS study's heuristic engines raise, and here the answer comes out on
the side of more, cheaper iterations, which is worth recording precisely because the
opposite is so often assumed.

## Acceptance: how much a non-improving move is allowed matters

Fix the loop and change only when a non-improving candidate is kept. Of the five
axes, this one moves the score the most after the destroy operator.

- **A strict hill-climb, which keeps only strict improvements, is the weakest, at
  a mean of 361.** Refusing every sideways move locks it into the first basin it
  finds; its accept rate is essentially zero.
- **Allowing equal-or-better moves (the anchor) does better, at 366.** The
  sideways moves let it drift across the equal-score plateaus that dominate this
  landscape.
- **A cooling simulated-annealing rule is the strongest acceptance by a clear
  margin, at 377 (best 394), among the best of the greedy-start variants.**
  Allowing occasional *worsening* moves early, then cooling, lets it leave a
  plateau that pure sideways drift is trapped on, and its best score keeps
  improving to around iteration twenty thousand rather than freezing in the first
  few thousand. A late-acceptance rule, which compares against the score some tens
  of iterations ago, lands between the two at 369.

So the acceptance rule is a real lever here, not a detail: strict to annealing is a
sixteen-point swing on the same loop (361 to 377). That is worth stating against a known
observation from the community's own ALNS tuning, that across a wide range of
annealing temperatures the final scores were essentially identical. The two are not
in conflict. That tuning was done on near-record boards, where the landscape is a
sea of equal-score plateaus and any temperature accepts almost everything; this
study's mediocre starting board still has real downhill structure to exploit, so
whether the rule will step downhill to escape a plateau genuinely matters. Which
acceptance rule wins, like which destroy operator wins, depends on how good the
board already is.

## Restart: neither perturbation moves the needle

Fix the loop and change only what happens once it stalls. Doing nothing lets the
run grind the same basin for the rest of the minute. A random *kick*, which
unplaces and randomly refills a couple of dozen cells when the best has not moved
for a while, and a *revert to the best board so far*, which re-attacks the
incumbent, are the two perturbations tested. Both land within a point of the
no-restart anchor (365 and 365, against the anchor's 366). This is a clean null
result: bolting a stall-detector and a perturbation onto the greedy-mismatch loop
does not help it, because the perturbation either throws away the structure that
made the board good (the kick) or returns to a board the same operator has already
stalled on (the revert). Neither turns the loop into a basin-escaper; on this
puzzle, escaping a basin needs a different move than perturb-and-repair, which is
exactly what the [rigidity wall](/research/why/rigidity-wall) and the
[σ-cycle structure](/research/why/sigma-cycles) explain.

## The through-line

Two themes run through the five comparisons. The first is that **the two decisions
that move the score are the destroy operator and the acceptance rule**, and both
move it in the same counterintuitive direction: the winning choices are the ones
that keep the loop *exploring* rather than *exploiting*. Random destroy beats every
operator that targets the breaks; annealing, which steps downhill to leave a
plateau, beats every rule that only moves sideways or uphill. Refining the refill
and bolting on a restart, the two decisions that try to be cleverer about a region
the loop is already stuck on, buy nothing.

The second is why exploring wins here and fixating wins on a near-record board:
**the repair loop is a basin explorer, not a basin escaper.** On a mediocre board
there is broad downhill structure everywhere, so the moves that cover more of it
win; on a near-record board there is none left but a single interlocking cycle, so
the moves that target it precisely win. Neither regime lets perturb-and-repair
escape a basin once it is in one. That is why the construct-then-refine pipelines
that reach this project's best boards divide the labour the way they do: a strong
constructive producer to choose a good basin, and repair as the last mile inside
it, never asked to climb out.

## Related

- [The repair study](https://eternity2.dev/research/lab/experiments/raphael-anjou/repair-study) — The sibling of the DFS study, for the other way people attack Eternity II: destroy part of a board, rebuild it, keep the change if it helps. One question, asked carefully. What does each decision in that loop buy: which region to destroy, how to rebuild it, when to keep a move, when to restart, and what board to start from?
- [How the study is built](https://eternity2.dev/research/lab/experiments/raphael-anjou/repair-study/method) — The engine behind the repair study: one composable destroy-and-repair loop where a variant is a declared change over a parent, the shared IO and scorer it sits on with the DFS study, an incrementally-maintained mismatch map, and the definitions of every statistic the study raises.
- [Local search and ALNS](https://eternity2.dev/research/build/local-search/local-search-alns) — Destroy part of a board, rebuild it better, and let the algorithm learn which demolitions pay. Adaptive large-neighborhood search is the most reliable polisher this project has, and the cleanest demonstration of the wall where polishing ends.